I should mention the recent failed attempt (by a vote of 30-1) of newly elected Texas Senator, and radio personality, Dan Patrick to change a long standing tradition in the Senate of requiring a 2/3rds vote in order for a bill to be considered on the Senate floor.
The purpose is to ensure that a degree of consensus exists on Senate bills by requiring a super-majority. This empowers a minority to defeat bills it objects to. Patrick argues that this is anti-democratic, which it is. Proponents argue that this is how minority rights can be protected in a majoritarian system.
